Meters using a Hall element magnetically coupled to a line current to generate an output voltage proportional to the instantaneous current, power or energy or other magnetic flux dependent parameter have been in existence for several years. These meters operate with good accuracy over only a limited temperature range, however, due to the high dependence of the Hall element output voltage on temperature. With reference to FIG. 1, measurement of the flux density B of a magnetic field associated with line current I.sub.L is made by applying a control current I.sub.C to the Hall element 10 and exposing the element to the magnetic field. A Hall voltage V.sub.H is developed across the output terminals of element 10 which are disposed at right angles to the flow direction of the control current. The flux density B of the field is determined from the Hall voltage V.sub.H on the basis of a predetermined mathematical relationship between the two parameters. A more detailed discussion of the theory underlying the Hall effect is found in Section 5.2 of Runyan, Semiconductor Measurements and Instrumentation, Texas Instruments Electronic Series, McGraw-Hill Book Company, 1975.
The Hall voltage V.sub.H of Hall element 10 can be defined by V.sub.H =K(T)I.sub.C B, wherein K(T) represents a temperature coefficient which depends upon the configuration of the Hall element, temperature and the like, I.sub.C represents the control current and B represents the flux density passing through the element in a direction perpendicular to the element plane.
The power in watts dissipated in a circuit is P=V (volts).times.I (amperes). Assuming that the control current I.sub.C applied to the Hall element is proportional to the line voltage (I.sub.C .alpha.V.sub.L), and since flux density B is proportional to line current (B.alpha.I.sub.L), Hall voltage V.sub.H is proportional to power. This relationship can be better understood from an analysis of the basic power and Hall voltage equations: EQU P.sub.L =I.sub.L V.sub.L ( 1)
where:
P.sub.L is line power, PA1 I.sub.L is line current, and PA1 V.sub.L is line voltage; and EQU V.sub.H =K(T)I.sub.C B (2) PA1 V.sub.H is Hall voltage, PA1 K(T) is a temperature dependent constant, PA1 I.sub.C is control current, and PA1 B is magnetic flux density;
where:
Since: EQU B=K.sub.1 I.sub.L ( 3)
and EQU I.sub.C =K.sub.2 V.sub.L ( 4)
combining equations (2), (3) and (4) yields: EQU V.sub.H =K(T)K.sub.1 K.sub.2 I.sub.L V.sub.L ( 5)
or EQU V.sub.H =KP.sub.L ( 6)
where: EQU K=K(T)K.sub.1 K.sub.2.
Line power is thus determined by exposing the Hall element to magnetic flux developed by line current while obtaining the Hall element control current from the line voltage. Similarly, line energy can be measured by integrating the Hall element voltage. Line current is typically determined by measuring Hall voltage while maintaining the control current I.sub.C constant.
As shown in FIG. 2, whereas the relationship between Hall voltage V.sub.H and magnetic flux density B is fairly linear at a fixed temperature T, FIG. 3 illustrates that the Hall voltage varies substantially as a function of temperature. The temperature of the Hall element in an operating environment is unpredictable since it is a function of ambient temperature and also of the magnitude of control current flowing through the element. The variation of Hall voltage with temperature at constant flux density is unacceptable in high accuracy power, energy or current measurement systems since this factor introduces error into any reading made at a temperature different from a reference or calibration temperature.
It is an object of the invention, therefore, to provide a system for compensing a Hall effect element for its dependency on temperature.
In Suzuki U.S. Pat. No. 4,099,238, the Hall voltage and a temperature dependent voltage are supplied to an analog calculation circuit which generates a temperature compensated signal proportional to magnetic flux density. The circuit solves an equation that involves a series approximation of a nonlinear relationship between Hall voltage and temperature. Because the equation is based on an approximation, there is error in the resultant flux density dependent signal. Also, since the circuit operates in the analog domain, it requires relatively expensive analog components such as multipliers, adders and subtractors. The number and cost of these components increase as the accuracy of the approximation on which the equation is based is increased. As another disadvantage, the circuit lacks versatility because the coefficients of the equation must be changed for each Hall element.
A further object of the invention, therefore, is to provide a temperature compensation system for a Hall element that is more accurate and less costly than the analog systems of the prior art.
An additional object of the invention is to provide a temperature compensation system for a Hall element that can be tailored to be operative with different elements.